Correcting mean-field approximations for birth-death-movement processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

Model-order selection in Zernike polynomial expansion of corneal surfaces using the efficient detection criterion

Corneal-height data are typically measured with videokeratoscopes and modeled using a set of orthogonal Zernike polynomials. We address the estimation of the number of Zernike polynomials, which is formalized as a model-order selection problem in linear regression. Classical information-theoretic criteria tend to overestimate the corneal surface due to the weakness of their penalty functions, while bootstrap-based techniques tend to underestimate the surface or require extensive processing. In this paper, we propose to use the efficient detection criterion (EDC), which has the same general form of information-theoretic-based criteria, as an alternative to estimating the optimal number of Zernike polynomials. We first show, via simulations, that the EDC outperforms a large number of information-theoretic criteria and resampling-based techniques. We then illustrate that using the EDC for real corneas results in models that are in closer agreement with clinical expectations and provides means for distinguishing normal corneal surfaces from astigmatic and keratoconic surfaces.

Robust mean super-resolution for less cooperative NIR iris recognition at a distance and on the move

Less cooperative iris identification systems at a distance and on the move often suffers from poor resolution. The lack of pixel resolution significantly degrades the iris recognition performance. Super-resolution has been considered to enhance resolution of iris images. This paper proposes a pixelwise super-resolution technique to reconstruct a high resolution iris image from a video sequence of an eye. A novel fusion approach is proposed to incorporate information details from multiple frames using robust mean. Experiments on the MBGC NIR portal database show the validity of the proposed approach in comparison with other resolution enhancement techniques.

Fast hole surface conduction observed for indoline sensitizer dyes immobilized at fluorine-doped tin oxide - TiO2 surfaces

The indoline dyes D102, D131, D149, and D205 have been characterized when adsorved on fluorine-doped tin oxide (FTO) and TiO2 electrode surfaces. Adsorption from 50:50 acetonitrile - tert-butanol onto flourine-doped tin oxide (FTO) allows approximate Langmuirian binding constants of 6.5 x 10(4), 2.01 x 10(3), 2.0 x 10(4), and 1.5 x 10(4) mol-1 dm3, respectively, to be determined. Voltammetric data obtained in acetonitrile/0.1 M NBu4PF6 indicate reversible on-electron oxidation at Emid = 0.94, 0.91, 0.88, and 0.88 V vs Ag/AgCI(3 M KCI), respectively, with dye aggregation (at high coverage) causing additional peak features at more positive potentials. Slow chemical degradation processes and electron transfer catalysis for iodine oxidation were observed for all four oxidezed indolinium cations. When adsorbed onto TiO2 nanoparticle films (ca. 9nm particle diameter and ca.3/um thickness of FTO0, reversible voltammetric responses with Emid = 1.08, 1.156, 0.92 and 0.95 V vs Ag/AgCI(3 M KCI), respectively, suggest exceptionally fast hole hopping diffusion (with Dapp > 5 x 10(-9) m2 s-1) for adsorbed layers of four indoline dyes, presumably due to pie-pie stacking in surface aggregates. Slow dye degradation is shown to affect charge transport via electron hopping. Spectrelectrochemical data for the adsorbed indoline dyes on FTO-TiO2 revealed a red-shift of absorption peaks after oxidation and the presence of a strong charge transfer band in the near-IR region. The implications of the indoline dye reactivity and fast hole mobility for solar cell devices are discussed.

Corrected mean-field models for spatially-dependent advection-diffusion-reaction phenomena

In the exclusion-process literature, mean-field models are often derived by assuming that the occupancy status of lattice sites is independent. Although this assumption is questionable, it is the foundation of many mean-field models. In this work we develop methods to relax the independence assumption for a range of discrete exclusion process-based mechanisms motivated by applications from cell biology. Previous investigations that focussed on relaxing the independence assumption have been limited to studying initially-uniform populations and ignored any spatial variations. By ignoring spatial variations these previous studies were greatly simplified due to translational invariance of the lattice. These previous corrected mean-field models could not be applied to many important problems in cell biology such as invasion waves of cells that are characterised by moving fronts. Here we propose generalised methods that relax the independence assumption for spatially inhomogeneous problems, leading to corrected mean-field descriptions of a range of exclusion process-based models that incorporate (i) unbiased motility, (ii) biased motility, and (iii) unbiased motility with agent birth and death processes. The corrected mean-field models derived here are applicable to spatially variable processes including invasion wave type problems. We show that there can be large deviations between simulation data and traditional mean-field models based on invoking the independence assumption. Furthermore, we show that the corrected mean-field models give an improved match to the simulation data in all cases considered.

Early osteogenic response of osteoprogenitor cells on modified titanium implant surfaces leads to improved osteogenesis

Background: Implant surface micro-roughness and hydrophilicity are known to improve the osteogenic differentiation potential of osteoprogenitor cells. This study was aimed to determine whether topographically and chemically modified titanium implant surfaces stimulate an initial osteogenic response in osteoprogenitor cells, which leads to their improved osteogenesis. ----- ----- Methods: Statistical analysis of microarray gene expression profiling data available from studies (at 72 hours) on sand-blasted, large grit acid etched (SLA) titanium surfaces was performed. Subsequently, human osteoprogenitor cells were cultured on SLActive (hydrophilic SLA), SLA and polished titanium surfaces for 24 hours, 3 days and 7 days. The expression of BMP2, BMP6, BMP2K, SP1, ACVR1, FZD6, WNT5A, PDLIM7, ITGB1, ITGA2, OCN, OPN, ALP and RUNX2 were studied using qPCR. ----- ----- Results: Several functional clusters related to osteogenesis were highlighted when genes showing statistically significant differences (from microarray data at 72 hours) in expression on SLA surface (compared with control surface) were analysed using DAVID (online tool). This indicates that differentiation begins very early in response to modified titanium surfaces. At 24 hours, ACVR1 (BMP pathway), FZD6 (Wnt pathway) and SP1 (TGF-β pathway) were significantly up-regulated in cultures on the SLActive surface compared to the other surfaces. WNT5A and ITGB1 also showed higher expression on the modified surfaces. Gene expression patterns on Day 3 and Day 7 did not reveal any significant differences.----- ----- Conclusion: These results suggest that the initial molecular response of osteoprogenitor cells to modified titanium surfaces may be responsible for an improved osteogenic response via the BMP and Wnt signalling pathways.

Mean and variance of estimates of the bispectrum of a harmonic random process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework